Problem 7-51 Energy cons.

A boy is playing with a rope tied to a tree near his favourite swimming hole. Initially the boy is stationary and the rope (of length \(3.7 \;m\)) makes an angle of \(48^\circ\) with the vertical. He then lifts his feet slightly and starts to swing freely. If air resistance is neglected, use conservation of energy to determine:

(a) his speed at the bottom of the swing
(b) the minimum height, relative to his initial position, to which he can swing.

Diagram of a tree on the edge of a cliff with water below. A rope hangs from a branch hanging over the water.

Where should the origin be chosen in this problem?

Diagram of angle of rope

(A)   Where the motion starts, i.e. at 1 in the drawing.

(B)   At the bottom of the swing, i.e. at 2 in the drawing.

(C)   At the top of the rope.